Lyapunov exponents from geodesic spread in configuration space

Year: 1997

Authors: Cerruti-Sola M., Franzosi R., Pettini M.

Autors Affiliation: Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, Firenze, 50125, Italy; Dipartimento di Fisica, Università di Firenze, Largo E. Fermi 5, Firenze, 50125, Italy; Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, Firenze, 50125, Italy

Abstract: The exact form of the Jacobi–Levi-Civita (JLC) equation for geodesic spread is here explicitly worked out at arbitrary dimension for the configuration space manifold [Formula Presented] of a standard Hamiltonian system, equipped with the Jacobi (or kinetic energy) metric [Formula Presented] As the Hamiltonian flow corresponds to a geodesic flow on [Formula Presented] the JLC equation can be used to study the degree of instability of the Hamiltonian flow. It is found that the solutions of the JLC equation are closely resembling the solutions of the standard tangent dynamics equation which is used to compute Lyapunov exponents. Therefore the instability exponents obtained through the JLC equation are in perfect quantitative agreement with usual Lyapunov exponents. This work completes a previous investigation that was limited only to two degrees of freedom systems.

Journal/Review: PHYSICAL REVIEW E

Volume: 56 (4)      Pages from: 4872  to: 4875

KeyWords: Choas; Differential Geometry; Dynamical Systems
DOI: 10.1103/PhysRevE.56.4872

Citations: 15
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